The role of directional compactness in the existence and computation of contingent epiderivatives

[摘要] This paper underlines the role of directional compactness in the scalarization of graphical derivatives of set-valued maps taking values in infinite-dimensional spaces. Two main theorems are given. The first one states the equivalence of contingent epiderivatives and tau(w)-contingent epiderivatives for directionally compact maps. The second main result proves a variational characterization for the contingent epiderivative or stable and directionally compact maps taking values in general image spaces, extending known results in finite-dimensional and reflexive Banach spaces. The hypotheses given are minimal as is shown by means of several examples. Connections of these theorems with other results of the literature are also provided. (C) 2010 Published by Elsevier Inc.

[发布日期] 2010-12-01

[关键词] Ordered spaces;Set-valued analysis;(tau(w)-)contingent derivatives;Epiderivatives;Fourier coefficients